A gapped ground state of a quantum spin system has a natural length scale set by the gap. This length scale governs the decay of correlations. A common intuition is that this length scale also controls the spatial relaxation towards the ground state away from impurities or boundaries. The aim of this article is to take a step towards a proof of this intuition. We assume that the ground state is frustration-free and invertible, i.e. it has no long-range entanglement. Moreover, we assume the property that we are aiming to prove for one specific kind of boundary condition; namely open boundary conditions. This assumption is also known as the "local topological quantum order" (LTQO) condition. With these assumptions we can prove stretched exponential decay away from boundaries or impurities, for any of the ground states of the perturbed system. In contrast to most earlier results, we do not assume that the perturbations at the boundary or the impurity are small. In particular, the perturbed system itself can have long-range entanglement.

中文翻译：

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可逆的、无挫折的基态对大扰动的稳定性

量子自旋系统的间隙基态具有由间隙设定的自然长度尺度。这个长度尺度控制相关性的衰减。一个常见的直觉是，这个长度尺度还控制着远离杂质或边界的向基态的空间弛豫。本文的目的是朝着证明这种直觉迈出一步。我们假设基态是无挫折和可逆的，即它没有长程纠缠。此外，我们假设我们旨在证明一种特定边界条件的性质；即开放边界条件。这个假设也被称为“局部拓扑量子序”（LTQO）条件。有了这些假设，我们可以证明远离边界或杂质的指数衰减，对于扰动系统的任何基态。与大多数早期结果相反，我们不假设边界或杂质处的扰动很小。特别是，受扰动的系统本身可能具有长程纠缠。